Determine the equation of the midline of the following graph.
Answer:
3
Step-by-step explanation:
midline is the distance or the midway between the highest point and the lowest one or between maximum and minimum,
for the given graph,
maximum point = 5
minimum point = 1
midline = 5 +1 / 2 = 6 / 2 = 3
Use the washer method to find the volume of revolution generated by revolving the region bounded by the graphs of y = 8√x,
y = 16, and the y-axis about the x-axis.
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
The volume of revolution generated by revolving the region about the x-axis is -512π.
To find the volume of revolution using the washer method, we need to integrate the area of the cross-sections formed by rotating the region bounded by the graphs of y = 8√x, y = 16, and the y-axis about the x-axis.
Let's start by setting up the integral. We will integrate with respect to x since the region is bounded by the x-axis.
The lower limit of integration (x) is 0, and the upper limit is found by setting y = 8√x equal to y = 16 and solving for x:
8√x = 16
√x = 2
x = 4
So the integral setup is:
V = ∫[0, 4] π(R^2 - r^2) dx
To find the outer radius (R), we consider the distance between the curve y = 8√x and the x-axis. Since we are revolving around the x-axis, R is simply y = 8√x.
The inner radius (r) is the distance between the line y = 16 and the x-axis, which is simply 16.
Now we can set up the integral:
V = ∫[0, 4] π((8√x)^2 - 16^2) dx
= ∫[0, 4] π(64x - 256) dx
Integrating:
V = π(32x^2 - 256x) |[0, 4]
= π[(32(4)^2 - 256(4)) - (32(0)^2 - 256(0))]
= π[512 - 1024 - 0]
= -512π
The volume of revolution generated by revolving the region about the x-axis is -512π.
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The commuting time (the average number of hours spent commuting each week) for students at a particular university is normally distributed with a mean of 63 mins and standard deviation of 9.61.
The probability that a randomly student at the university has a commuting time between 55 and 70 mins is about:
The probability that a randomly student at the university has a commuting time between 55 and 70 mins is about 0.56. Given information:The commuting time (the average number of hours spent commuting each week) for students at a particular university is normally distributed with a mean of 63 mins and standard deviation of 9.61.
Find: We are to determine the probability that a randomly student at the university has a commuting time between 55 and 70 mins.
Here,μ = 63 min σ = 9.61 min. We have to find the probability of a random student has commuting time between 55 and 70 min. That is P(55 ≤ X ≤ 70).First, we need to convert the given range to Standard Normal Distribution form.i.e., z-score for X = 55 and X = 70.Z-score formula:z = (X - μ) / σFor X = 55z = (55 - 63) / 9.61z = -0.83For X = 70z = (70 - 63) / 9.61z = 0.73. We need to find the probability of a random student has a z-score between -0.83 and 0.73.P(-0.83 < z < 0.73)
Using standard normal table or calculator, we can find the probability P(-0.83 < z < 0.73) = P(z < 0.73) - P(z < -0.83)= 0.7665 - 0.2033≈ 0.56
Thus, the probability that a randomly student at the university has a commuting time between 55 and 70 mins is about 0.56.
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Trent has an 8-foot tall tent in the shape of square based pyramid with a base length of 14 feet. If one bottle of waterproof spray covers 76 square feet, how many bottles will he need to waterproof his tent.
Trent will need approximately 2.86 bottles of waterproof spray to cover his tent.
To calculate the number of bottles of waterproof spray Trent will need to cover his tent, we first need to find the surface area of the tent.
The surface area of a square-based pyramid is given by the formula:
Surface Area = Base Area + (0.5 x Perimeter of Base x Slant Height)
The base of the pyramid is a square with a side length of 14 feet, so the base area is:
Base Area = (Side Length)^2 = 14^2 = 196 square feet
To find the slant height of the pyramid, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle formed by one side of the base, the height of the pyramid, and the slant height. The height of the pyramid is given as 8 feet, and half the length of the base is 7 feet.
Using the Pythagorean theorem:
[tex]Slant Height^2 = (Half Base Length)^2 + Height^2[/tex]
[tex]Slant Height^2 = 7^2 + 8^2Slant Height^2 = 49 + 64Slant Height^2 = 113Slant Height ≈ √113 ≈ 10.63 feet[/tex]
Now we can calculate the surface area of the tent:
Surface Area = 196 + (0.5 x 4 x 10.63)
Surface Area = 196 + (2 x 10.63)
Surface Area = 196 + 21.26
Surface Area ≈ 217.26 square feet
Since each bottle of waterproof spray covers 76 square feet, we can divide the total surface area of the tent by the coverage of each bottle to find the number of bottles needed:
Number of Bottles = Surface Area / Coverage per Bottle
Number of Bottles = 217.26 / 76
Number of Bottles ≈ 2.86
Therefore, Trent will need approximately 2.86 bottles of waterproof spray to cover his tent. Since we can't have a fraction of a bottle, he will need to round up to the nearest whole number. Therefore, Trent will need 3 bottles of waterproof spray to fully waterproof his tent.
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A shoes delear net birr 8000 worth of shoes from a shoe company.Then,find the amount it is to pay including VAT
The total amount to pay would be 8800 Ethiopian Birr.
To find the amount to pay including VAT, we need to know the applicable VAT rate. VAT, or Value Added Tax, is a consumption tax added to the value of goods and services. The VAT rate can vary from country to country or even within different regions.
Assuming a VAT rate of 10%, we can calculate the VAT amount by multiplying the net value of the shoes by the VAT rate. In this case, the net value of the shoes is 8000 Ethiopian Birr. Therefore, the VAT amount would be 8000 * 0.10 = 800 Ethiopian Birr.
To find the total amount to pay including VAT, we add the VAT amount to the net value of the shoes. Thus, the total amount to pay would be 8000 + 800 = 8800 Ethiopian Birr.
It's important to note that the VAT rate and regulations can vary, so it's always advisable to check the specific VAT rate applicable in a given country or region. Additionally, different goods and services may have different VAT rates or exemptions, so it's crucial to consider the specific rules governing the shoe industry in the relevant jurisdiction.
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What is the value of x? Triangle ABC. Segment AD bisects angle A. The length of side AB is 28. The length of segment BD is 14. The length of side AC is 25. The length of segment CD is unknown and is labeled x. Enter your answer, as a decimal, in the box. x =
Answer:
Step-by-step explanation:
To find the value of x, we can use the Angle Bisector Theorem, which states that in a triangle, a line segment that bisects an angle divides the opposite side into segments that are proportional to the other two sides.
In this case, segment AD bisects angle A, so we can set up the following proportion:
BD/DC = AB/AC
Plugging in the given values, we have:
14/DC = 28/25
To solve for DC (segment CD), we can cross-multiply:
28 * DC = 14 * 25
Simplifying further:
DC = (14 * 25) / 28
DC ≈ 12.5
Therefore, the length of segment CD is approximately 12.5.
help me please.. please
Step-by-step explanation:
Parallel to the x-axis means it is just a horizontal line with the value being the y-coordinate of the point:
y = -2
Answer:
y=-2
and m=0 must be your answer
Step-by-step explanation:
as line is parallel to x axis its slope will be zero as it does not have any definite x coordinate
so
equation of line is y-y'=m(x-x')
so m=0 m is slope
y'=-2 and x'=4
so by substituting the values
y+2=0
so y=-2
and m=0 is your answer
omari's monthly taxable income is ksh 24200. calculate the tax charged on omari's monthly earning
The tax charged on Omari's monthly earning of Ksh 24,200 is Ksh 3,340.
To calculate the tax charged on Omari's monthly earning, we need to consider the tax brackets and rates applicable in the specific tax system or country. Since you haven't specified a particular tax system, I will provide a general explanation.
Assuming we have a simplified progressive tax system with three tax brackets:
For the first tax bracket, let's say income up to Ksh 10,000 is taxed at a rate of 10%.
For the second tax bracket, income between Ksh 10,001 and Ksh 20,000 is taxed at a rate of 15%.
For the third tax bracket, income above Ksh 20,000 is taxed at a rate of 20%.
To calculate the tax charged on Omari's monthly earning of Ksh 24,200, we can divide it into the respective tax brackets:
Ksh 10,000 falls in the first tax bracket. So, the tax for this portion is 10% of Ksh 10,000, which is Ksh 1,000.
Ksh 20,000 - Ksh 10,000 = Ksh 10,000 falls in the second tax bracket. The tax for this portion is 15% of Ksh 10,000, which is Ksh 1,500.
The remaining amount, Ksh 24,200 - Ksh 20,000 = Ksh 4,200, falls in the third tax bracket. The tax for this portion is 20% of Ksh 4,200, which is Ksh 840.
Now, we can sum up the taxes for each bracket:
Total Tax = Tax in the first bracket + Tax in the second bracket + Tax in the third bracket
Total Tax = Ksh 1,000 + Ksh 1,500 + Ksh 840
Total Tax = Ksh 3,340
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Charmaine is buying a new car. Her bank offers her a loan of $20,000 with a 6.25% annual interest rate compounded quarterly, or every 3 months. Which of the following equations could model the bank’s offer? Select all that apply.
Answer:
[tex]{A = 20000(1 + \frac{0.0625}{4})^{4t}}[/tex]
Step-by-step explanation:
The question asks us to find an expression for compound interest for the given scenario.
To do this, we have to use the following formula for compound interest:
[tex]\boxed{A = P(1 + \frac{r}{n})^{nt}}[/tex]
where:
• A ⇒ final amount
• P ⇒ principal amount = $20,000
• r ⇒ interest rate (decimal) = [tex]\frac{6.25}{100}[/tex] = 0.0625
• n ⇒ number of times interest is compounded per year = 4
• t ⇒ time in years
Therefore, if we substitute the data above into the formula, we can find the required expression:
[tex]{A = 20000(1 + \frac{0.0625}{4})^{4t}}[/tex]
SOMEONE SOLVE THUS PLEASE ILL GIVE U THIRTY BRAINILY POINTS U WILL BE RICH PLEACE ANSWER I AM IN DESPERATE NEED THANK YOU SO MUCH
The degree of f(x) is 5, and the leading coefficient is negative. There are 3 distinct real zeros and 2 relative maximum values.
How to obtain the zeros of a function?From the graph of a function, the zeros of the function are the x-intercepts, that is, the values of x for which the graph crosses or touches the x-axis.
The function in this problem has three distinct zeros, given as follows:
2 with even multiplicity, as the graph turns at the x-axis.1 with odd multiplicity, as the graph crosses the x-axis.Hence the degree of the function is given as follows:
2 x 2 + 1 = 5.
The leading coefficient is negative, as the function has an odd degree, but increases to left and decreases to right.
The relative maximums of the functions are the points where the function makes a downward turn, changing from increasing to decreasing, hence there are two points.
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What is the z score for Brazil?
The z-score for Brazil is given as follows:
Z = 0.87.
What is the z-score formula?The z-score formula is defined as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In which:
X is the measure.[tex]\mu[/tex] is the population mean.[tex]\sigma[/tex] is the population standard deviation.The parameters for this problem are given as follows:
[tex]X = 6.24, \mu = 4.8, \sigma = 1.66[/tex]
Hence the z-score for Brazil is given as follows:
Z = (6.24 - 4.8)/1.66
Z = 0.87.
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Find the net area of the following curve on the interval [0, 2].
(SHOW WORK)
f(x) = ex - e
The net area of the curve represented by f(x) = ex - e on the interval [0, 2] is e2 - 1.
To find the net area of the curve represented by the function f(x) = ex - e on the interval [0, 2], we need to calculate the definite integral of the function over that interval. The net area can be determined by taking the absolute value of the integral.
The integral of f(x) = ex - e with respect to x can be computed as follows:
∫[0, 2] (ex - e) dx
Using the power rule of integration, the antiderivative of ex is ex, and the antiderivative of e is ex. Thus, the integral becomes:
∫[0, 2] (ex - e) dx = ∫[0, 2] ex dx - ∫[0, 2] e dx
Integrating each term separately:
= [ex] evaluated from 0 to 2 - [ex] evaluated from 0 to 2
= (e2 - e0) - (e0 - e0)
= e2 - 1
The net area of the curve represented by f(x) = ex - e on the interval [0, 2] is e2 - 1.
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What is the answer? As the last one is incorrect
The best measure of center of the data is (a) mean; because the data are close together
How to determine the best measure of center of the dataFrom the question, we have the dataset of 10 values
In the given dataset, we can see that there are no outliers present in the dataset
By definition, outliers are extreme values.
Since there are no outliers, it means that the mean is the best measure of center
This is because the mean is affected by the presence of outliers and since no outlier is present, we use the mean
From the list of options, we have the mean value to be 42.536
Hence, the true statement is (a)
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The product of 3, and a number increased by -7, is -36
┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈
✦ The number is - 5
┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈
[tex]\begin{gathered} \; \sf{\color{pink}{Let \; the \; other \; number \; be \; (x)::}} \\ \end{gathered}[/tex]
Atq,,
[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3 \times \bigg \lgroup \: x + ( - 7) \bigg \rgroup = - 36} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3 \times \bigg \lgroup \: x - 7 \bigg \rgroup = - 36} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3x - 21 = - 36} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3x = - 36 + 21} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3x = - 15} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{x = \dfrac{\cancel{ - 15}}{\cancel{ \: 3}}} \qquad \bigg \lgroup \sf{Cancelling \: by \: 3} \bigg \rgroup \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{pink} :\dashrightarrow \underline{\color{pink}\boxed{\colorbox{black}{x = - 5}}} \: \pmb{\bigstar} \\ \\ \end{gathered}[/tex]
The answer is:
z = -5Work/explanation:
The product means we multiply two numbers.
Here, we multiply 3 and a number increased by -7; let that number be z.
So we have
[tex]\sf{3(z+(-7)}[/tex]
simplify:
[tex]\sf{3(z-7)}[/tex]
This equals -36
[tex]\sf{3(z-7)=-36}[/tex]
[tex]\hspace{300}\above2[/tex]
[tex]\frak{solving~for~z}[/tex]
Distribute
[tex]\sf{3z-21=-36}[/tex]
Add 21 on each side
[tex]\sf{3z=-36+21}[/tex]
[tex]\sf{3z=-15}[/tex]
Divide each side by 3
[tex]\boxed{\boxed{\sf{z=-5}}}[/tex]
Calc II Question
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x axis
x = 4y^2 - y^3
x = 0
Sam’s Swimming Pool Cleaning has an annual gross profit of $88,400. Sam charges $25 per week for each of his customers for 52 weeks. His annual operating expenses, including labor and supplies, are $48,000. How many customers does Sam’s Swimming Pool Cleaning have?
a.
17
b.
35
c.
68
d.
105
Answer:
D.
Step-by-step explanation:
To find the number of customers Sam's Swimming Pool Cleaning has, we need to calculate the total revenue generated by the business and divide it by the weekly charge per customer.
Total revenue = 52 x $25 x number of customers
We know that the annual gross profit is $88,400. So, we can set up an equation to find the number of customers:
$88,400 = 52 x $25 x number of customers - $48,000
$88,400 + $48,000 = 52 x $25 x number of customers
$136,400 = $1,300 x number of customers
Number of customers = $136,400/$1,300
Number of customers = 105
Therefore, Sam's Swimming Pool Cleaning has 105 customers. The correct answer is D.
Sam’s Swimming Pool Cleaning have 105 customers.
What is an expression?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is:
To get how many customers Sam has, write an equation that will relate to the gross profit. Let n be the customers. Since for 52 weeks, Sam charges $25 per week per person, multiply n by the number of weeks and the charge. The equation is written as $88,400 = 52 weeks x $25 per week x n persons. Divide $88,400 by the product of 52 weeks and the $25 charge. The answer will be 105.
Therefore, Sam’s Swimming Pool Cleaning have 105 customers.
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Suppose 150 mL (milliliters) of a medication is administered to an infected patient. It is estimated that 8%
of this person’s cells are infected with a virus.
1. Suppose 2 mL of the medication contains 2.3 × 103 antiviral proteins. How many antiviral proteins were
injected into this person? Express your answer in scientific notation.
2. There are about 1 × 1014 cells in the average adult human body. What percentage of this person’s cells
can be affected by the administered medication?
3. How many mL of medication would need to be administered to the patient in order to have 1 antiviral
protein for every infected cell? How many liters is this equivalent to?
Answer:
Step-by-step explanation:
To find the number of antiviral proteins injected into the person, we can set up a proportion:
2 mL contains 2.3 × 10^3 antiviral proteins
x mL contains how many antiviral proteins?
The proportion can be written as:
2 mL / 2.3 × 10^3 = x mL / (unknown number of antiviral proteins)
We can solve this proportion by cross-multiplication:
2 mL * (unknown number of antiviral proteins) = 2.3 × 10^3 antiviral proteins * x mL
x = (2.3 × 10^3 antiviral proteins * x mL) / 2 mL
Simplifying, we get:
x = 1.15 × 10^3 * x mL
Therefore, the number of antiviral proteins injected into the person is 1.15 × 10^3.
The total number of cells in the person's body is approximately 1 × 10^14. If 8% of the person's cells are infected with the virus, we can calculate the percentage of cells that can be affected by the medication:
Percentage of cells affected = (Number of infected cells / Total number of cells) * 100
Number of infected cells = 8% of 1 × 10^14 cells
Number of infected cells = (8/100) * 1 × 10^14
Number of infected cells = 8 × 10^12
Percentage of cells affected = (8 × 10^12 / 1 × 10^14) * 100
Percentage of cells affected = 8 × 10^-2 * 100
Percentage of cells affected = 8%
Therefore, the administered medication can affect 8% of the person's cells.
To find the amount of medication needed to have 1 antiviral protein for every infected cell, we can set up a proportion:
2.3 × 10^3 antiviral proteins in 2 mL
1 antiviral protein in x mL
The proportion can be written as:
2.3 × 10^3 antiviral proteins / 2 mL = 1 antiviral protein / x mL
We can solve this proportion by cross-multiplication:
(2.3 × 10^3 antiviral proteins) * x mL = 2 mL * 1 antiviral protein
x = (2 mL * 1 antiviral protein) / (2.3 × 10^3 antiviral proteins)
Simplifying, we get:
x = 0.8696 mL
Therefore, to have 1 antiviral protein for every infected cell, approximately 0.8696 mL of medication needs to be administered. This is equivalent to 0.0008696 liters.
Read the following statements.
Statement 1: "If she is stuck in traffic, then she is late."
Statement 2: "If she is late, then she is stuck in traffic."
Statement 3: "If she is not late, then she is not stuck in traffic."
Meg writes, "Statement 3 is the inverse of statement 2 and contrapositive of statement 1."
Cassandra writes, "Statement 2 is the converse of statement 1 and inverse of statement 3."
Who is correct?
Both Meg and Cassandra are incorrect.
Only Meg is correct.
Both Meg and Cassandra are correct.
Only Cassandra is correct.
`Both Meg and Cassandra are incorrect in their assessments (option a).
Meg and Cassandra have both misunderstood the logical relationships between the statements. Let's analyze each statement and compare their claims:
Statement 1: "If she is stuck in traffic, then she is late."
Statement 2: "If she is late, then she is stuck in traffic."
Statement 3: "If she is not late, then she is not stuck in traffic."
Meg's claims: Meg states that Statement 3 is the inverse of Statement 2 and the contrapositive of Statement 1. However, this is incorrect. The inverse of Statement 2 would be "If she is not stuck in traffic, then she is not late," and the contrapositive of Statement 1 would be "If she is not late, then she is not stuck in traffic." So Meg's analysis is incorrect.
Cassandra's claims: Cassandra states that Statement 2 is the converse of Statement 1 and the inverse of Statement 3. However, this is also incorrect. The converse of Statement 1 would be "If she is late, then she is stuck in traffic," and the inverse of Statement 3 would be "If she is late, then she is stuck in traffic." So Cassandra's analysis is incorrect as well.
Therefore, both Meg and Cassandra are wrong in their assessments. The correct logical relationships are as follows:
- The contrapositive of Statement 1 is Statement 3.
- The converse of Statement 1 is Statement 2.
Hence, the correct answer is that both Meg and Cassandra are incorrect.
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Qué porcentaje de 200 es 164
A boat is traveling in a river that is floating downstream at a speed of 10 km/h. the boat can travel 40 km upstream in the same time it would take to travel 80 km down the stream. what is the speed of the boat in Still water?
The speed of the boat in still water is 3 times the speed of the river current.
To find the speed of the boat in still water, we can use the concept of relative motion and the given information about the boat's speed while traveling upstream and downstream.
Let's assume the speed of the boat in still water is "v" km/h, and the speed of the river current is "c" km/h.
When the boat is traveling upstream, it moves against the current, so its effective speed is reduced.
The boat's speed relative to the ground is given by (v - c) km/h.
Similarly, when the boat is traveling downstream, it moves with the current, so its effective speed is increased.
The boat's speed relative to the ground is given by (v + c) km/h.
According to the problem, the boat can travel 40 km upstream in the same time it would take to travel 80 km downstream.
Since time is constant in both cases, we can set up the following equation:
40/(v - c) = 80/(v + c)
To solve this equation, we can cross-multiply and simplify:
40(v + c) = 80(v - c)
40v + 40c = 80v - 80c
40c + 80c = 80v - 40v
120c = 40v
Dividing both sides by 40, we get:
3c = v.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
BC = 24 (D)
Step-by-step explanation:
Special Right Triangles (30-60-90 triangle)
5 Which of the following is the simplified form of the expression 15x - 12 - 4x + 3x + 13? O 14x+1 O 14x-1 O-14x+1 O-14x-1 4 Skip >> 4/10 complete
The simplified form of the expression 15x - 12 - 4x + 3x + 13 is 14x+1. Option A
To simplify the expression 15x - 12 - 4x + 3x + 13, we can combine like terms. Like terms are those that have the same variable and exponent.
First, let's combine the x terms:
15x - 4x + 3x = (15 - 4 + 3)x = 14x
Next, let's combine the constant terms:
-12 + 13 = 1
Putting it all together, the simplified form of the expression is:
14x + 1
Therefore, the correct answer is "14x + 1."
To simplify the expression, we added the coefficients of the x terms (15, -4, 3) to get 14x. Then, we added the constant terms (-12, 13) to get 1. This final expression, 14x + 1, does not have any like terms that can be combined further, so it is considered simplified.
It's important to note that when simplifying expressions, we group like terms together and perform the indicated operations, such as addition or subtraction. By doing so, we reduce the expression to its simplest form, where no further combining of like terms is possible.
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Shelley was playing her favorite video game. Her character started with 100 health points, but lost 11 when she got in a fight. She lost 12 more health points when a monster attacked her. Luckily, a healing spell gave her 21 health points back.
Shelley works out that she now has 98 health points. Does that sound about right?
Answer: 98 This statement is true
Step-by-step explanation:
100-11=89
89-12=77
77+21=98
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:B
Step-by-step explanation:
Question 8 of 10
How does the graph of f (x) = 3 (4)2-5 + 3 relate to its parent function?
A. The parent function has been 'stretched.
B. The parent function has been translated to the right.
C. The parent function has been translated up.
D. The parent function has been compressed.
Answer:
The correct answer is D. The graph of f(x) = 3(4)² - 5 + 3 is a transformation of the parent function. The parent function is y = x², which is a simple quadratic function.
In the given equation, the number 4 inside the parentheses represents a horizontal compression or shrink of the graph. The factor of 3 outside the parentheses represents a vertical stretch or expansion. The constant term -5 represents a vertical translation down by 5 units, and the constant term 3 represents a vertical translation up by 3 units.
Therefore, the graph of f(x) = 3(4)² - 5 + 3 is a compressed version of the parent function y = x², shifted down by 5 units and then shifted up by 3 units.
In circle O, secants ADB and AEC are drawn from external point A
such that points D, B, E, and C are on circle O. If AD = 8, AE = 6,
and EC is 12 more than BD, the length of BD is
(1) 6
(2) 22
(3) 36
(4) 48
The length of BD is 22.
In the given scenario, let's consider the following information.
AD = 8
AE = 6
EC is 12 more than BD.
To find the length of BD, we can utilize the Intercepted Arcs Theorem, which states that when two secants intersect outside a circle, the measure of an intercepted arc formed by those secants is equal to half the difference of the measures of the intercepted angles.
From the given information, we know that AD = 8 and AE = 6.
Since these are the lengths of the secants, we can use them to calculate the intercepted arcs.
First, let's find the intercepted arc corresponding to AD:
Intercepted Arc ADB = 2 [tex]\times[/tex] AD = 2 [tex]\times[/tex] 8 = 16
Similarly, we can find the intercepted arc corresponding to AE:
Intercepted Arc AEC = 2 [tex]\times[/tex] AE = 2 [tex]\times[/tex] 6 = 12
Now, we know that EC is 12 more than BD.
Let's assume the length of BD as x.
BD + 12 = EC
Now, let's consider the intercepted arcs theorem:
Intercepted Arc ADB - Intercepted Arc AEC = Intercepted Angle B - Intercepted Angle C
16 - 12 = Angle B - Angle C
4 = Angle B - Angle C.
Since Angle B and Angle C are vertical angles, they are congruent:
Angle B = Angle C.
Therefore, we can say:
4 = Angle B - Angle B
4 = 0
However, we have reached an inconsistency here.
The equation does not hold true, indicating that the given information is not consistent or there may be an error in the problem statement.
As a result, we cannot determine the length of BD based on the given information.
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if f(x) = 2x+7 then find f(x+2)
The answer is:
↬ f(x + 2) = 2x + 11
Work/explanation:
To evaluate the function, plug in x + 2 for x:
[tex]\boxed{\large\begin{gathered}\sf{f(x)=2x+7}\\\\\bf{distribute}\\sf{f(x+2)=2(x+2)+7}\\\\\bf{simplify}\\\sf{f(x+2)=2x+4+7}\\\\\sf{f(x+2)=2x+11}\end{gathered}}[/tex]
Hence, f(x +2) = 2x + 11.If � 1 = 4 a 1 =4 and � � = � � � − 1 + 4 a n =na n−1 +4 then find the value of � 5 a 5 .
The value of `a5 = λ5 = 824`.Therefore, the value of `a5` is 824.
Given the following values; `λ1 = 4` and `λn = na(n-1) + 4`.
We are required to calculate the value of `λ5` which is `a5`.
Solution We are given that;`λ1 = 4` which can also be expressed as `a1 = 4`. We are also given that `λn = na(n-1) + 4`. For `n=2`, `λ2 = 2a1 + 4 = 2(4) + 4 = 12`.
For `n=3`, `λ3 = 3a2 + 4 = 3(12) + 4 = 40`. For `n=4`, `λ4 = 4a3 + 4 = 4(40) + 4 = 164`. For `n=5`, `λ5 = 5a4 + 4 = 5(164) + 4 = 824`.
Hence, the value of `a5 = λ5 = 824`.Therefore, the value of `a5` is 824.
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given f(x) = x^3 - 10x + k, and the remainder when f(x) is divided by x + 3 is 6, then what is the value of K?
Answer:
Step-by-step explanation:
(x^3 - 10x + K)/(X+3) = 6 GIVEN
for different values of x there are many possible values of k some i will show
when we substitute x=1
we get k=33
at x=2
weget k=42
so many values are possible for k
because there is no intervel in question which restrics us from taking different values of x or k so you take any value of x you will get different values of k
A population of a particular yeast cell develops with a constant relative growth rate of 0.4465 per hour. The initial population consists of 3.3 million cells. Find the population size (in millions of cells) after 4 hours. (Round your answer to one decimal place.)
Starting with an initial population of 3.3 million yeast cells and a constant relative growth rate of 0.4465 per hour, the population size reaches approximately 5.892 million cells after 4 hours.
To calculate the population size after 4 hours, we can use the formula for exponential growth:
Population size = Initial population * [tex](1 + growth rate)^t^i^m^e[/tex]
Given that the initial population is 3.3 million cells and the relative growth rate is 0.4465 per hour, we can plug in these values into the formula:
Population size = 3.3 million *[tex](1 + 0.4465)^4[/tex]
Calculating the exponent first:
[tex](1 + 0.4465)^4 = 1.4465^4[/tex] ≈ 1.7879
Now, we can substitute this value back into the formula:
Population size = 3.3 million * 1.7879
Calculating the population size:
Population size = 5.892 million
Therefore, the population size after 4 hours is approximately 5.892 million cells.
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